The rate of rotation of a moving body about an axis may be determined by mounting an accelerometer on a frame and dithering it, with the accelerometer's sensitive axis and the direction of motion of the frame both normal to the rate axis about which rotation is to be measured. For example, consider a set of orthogonal axes X, Y and Z oriented with respect to the moving body. Periodic movement of the accelerometer along the Y axis of the moving body with its sensitive axis aligned with the Z axis results in the accelerometer experiencing a Coriolis acceleration directed along the Z axis as the moving body rotates about the X axis. A Coriolis acceleration is that perpendicular acceleration developed while the body is moving in a straight line, while the frame on which it is mounted rotates. This acceleration acting on the accelerometer is proportional to the velocity of the moving sensor body along the Y axis and its angular rate of rotation about the X axis. An output signal from the accelerometer thus includes a DC or slowly changing component or force signal F representing the linear acceleration of the body along the Z axis, and a periodic component or rotational signal .OMEGA. representing the Coriolis acceleration resulting from rotation of the body about the X axis.
The amplitude of that Coriolis component can be produced by vibrating the accelerometer, causing it to dither back and forth along a line perpendicular to the input axis of the accelerometer. Then, if the frame on which the accelerometer is mounted is rotating, the Coriolis acceleration component of the accelerometer's output signal will be increased proportional to the dither velocity. If the dither amplitude and frequency are held constant, then the Coriolis acceleration is proportional to the rotation rate of the frame.
The linear acceleration component and the rotational component representing the Coriolis acceleration may be readily separated by using two accelerometers mounted in back-to-back relationship to each other and processing their out put signals by sum and difference techniques. In U.S. Pat. No. 4,510,802, assigned to the assignee of this invention, two accelerometers are mounted upon a parallelogram with their input axes pointing in opposite directions. An electromagnetic D'Arsonval coil is mounted on one side of the parallelogram structure and is energized with a periodically varying current to vibrate the accelerometers back and forth in a direction substantially normal to their sensitive or input axis. The coil causes the parallelogram structure to vibrate, dithering the accelerometers back and forth. By taking the difference between the two accelerometer outputs, the linear components of acceleration are summed. By taking the sum of the two outputs, the linear components cancel and only the Coriolis or rotational components remain.
U.S. Pat. No. 4,509,801, commonly assigned to the assignee of this invention, describes the processing of the output signals of two accelerometers mounted for periodic, dithering motion to obtain the rotational rate signal .OMEGA. and the force or acceleration signal F representing the change in velocity, i.e. acceleration of the moving body, along the Z axis. U.S. Pat. No. 4,510,802, commonly assigned to the assignee of this invention, describes a control pulse generator, which generates and applies a sinusoidal signal of a frequency .omega. to the D'Arsonval coil to vibrate the parallelogram structure and thus the first and second accelerometer structures mounted thereon, with a dithering motion of the same frequency .omega.. The accelerometer output signals are applied to a processing circuit, which sums the accelerometer output signals to reinforce the linear components indicative of acceleration. The linear components are integrated over the time period T of the frequency .omega. corresponding to the dither frequency to provide the force signal F, which represents the change in velocity, i.e. acceleration, along the Z axis. The accelerometer output signals are also summed, whereby their linear components cancel and their Coriolis components are reinforced to provide a signal indicative of frame rotation. That difference signal is multiplied by a zero mean periodic function sgnc .omega.t. The resulting signal is integrated over a period T of the frequency .omega. by a sample and hold circuit to provide the signal .OMEGA. representing the rate of rotation of the frame.
The D'Arsonval coil is driven by a sinusoidal signal of the same frequency .omega. which corresponded to the period T in which the linear acceleration and Coriolis component signals were integrated. In particular, the pulse generator applies a series of pulses at the frequency .omega. to a sine wave generator, which produces the substantially sinusoidal voltage signal to be applied to the D'Arsonval coil. A pair of pick-off coils produce a feedback signal indicative of the motion imparted to the accelerometers. That feedback signal is summed with the input sinusoidal voltage by a summing junction, whose output is applied to a high gain amplifier. the output of that amplifier in turn is applied to the D'Arsonval type drive coil. The torque output of the D'Arsonval coil interacts with the dynamics of the parallelogram structure to produce the vibrating or dither motion. In accordance with well known servo theory, the gain of the amplifier is set high so that the voltage applied to the summing junction and the feedback voltage are forced to be substantially equal and the motion of the mechanism will substantially follow the drive voltage applied to the summing junction.
U.S. Pat. No. 4,881,408 describes the use of vibrating beam force transducers in accelerometers. In U.S. Pat. No. 4,372,173, the force transducer takes the form of a double-ended tuning fork fabricated from crystalline quartz. The transducer comprises a pair of side-by-side beams which are connected to common mounting structures at their ends. Electrodes are deposited on the beams and a drive circuit applies a periodic voltage signal to the electrodes causing the beams to vibrate toward and away from one another, 180 degrees out of phase. In effect, the drive circuit and beams form an oscillator with the beams playing the role of a frequency controlled crystal, i.e. the mechanical resonance of the beams controls the oscillation frequency. The vibrating beams are made of crystalline quartz, which has piezoelectric properties. Application of periodic drive voltages to such beams cause them to vibrate toward and away from one another, 180 degrees out of phase. When the beams are subjected to accelerating forces, the frequency of the mechanical resonance of the beams changes, which results in a corresponding change in the frequency of the drive signal. When subjected to acceleration forces that cause the beams to be placed in tension, the resonance frequency of the beams and thus the frequency of the drive signal increases. Conversely, if the beams are placed in a compression by the acceleration forces, the resonance frequency of the beams and the frequency of the drive signal is decreased.
Above referenced U.S. Pat. No. 5,005,413 describes accelerometers using vibrating force transducers require materials with low internal damping, to achieve high Q values that result in low drive power, low self-heating and insensitivity to electronic component variations. Transducer materials for high-accuracy instruments also require extreme mechanical stability over extended cycles at high stress levels. Crystalline silicon posses high Q values, and with the advent of low cost, micromachined mechanical structures fabricated from crystalline silicon, it is practical and desirable to create vibrating beams from a silicon substrate. Commonly assigned U.S. Pat. No. 4,912,990 describes a vibrating beam structure fabricated from crystalline silicon and including an electric circuit for applying a drive signal or current along a current path that extends in a first direction along a first beam and in a second, opposite direction along a second beam parallel to the first. A magnetic field is generated that intersects substantially perpendicular the conductive path, whereby the first and second beams are caused to vibrate towards and away from one another, 180 degrees out of phase.
Digital techniques employ stable, high frequency crystal clocks to measure a frequency change as an indication of acceleration forces applied to such vibrating beam accelerometers. To ensure precise integration or cosine demodulation, a crystal clock is used to set precisely the frequency of the dither drive signal. Outputs from two accelerometers are fed into counters to be compared to a reference clock signal produced by the crystal clock. A microprocessor reads the counters and processes the data to provide a force signal F and a rotational signal .OMEGA.. The main advantage of digital processing is the ability to demodulate with extreme precision. The short term stability of the reference crystal clock allows the half cycle time basis to be precisely equal. Thus a constant input to the cosine demodulator is chopped up into equal, positive half cycle and negative half cycle values, whose sum is exactly zero.
In an illustrative embodiment, the two accelerometers signals are counted in their respective counters over 100 Hz period (corresponding to a 100 Hz of the dither frequency .omega.) and are sampled at a 400 Hz data rate corresponding to each quarter cycle of the dither motion. The two accumulated counts are subtracted to form the force signal F. Since the counters act as an integrator, the acceleration signal is changed directly to a velocity signal. Taking the difference of the acceleration signals tends to reject all Coriolis signals as does the counter integration and locked period data sampling.
The Coriolis signals are detected by a cosine demodulation. The cosine demodulated signals from the first and second accelerometers are summed to produce the .DELTA..theta. signal. Again, the counters integrate the rate data to produce an angle change. The sum also eliminates any linear acceleration and the demodulation cancels any bias source including bias operating frequency and accelerometer bias. The accelerometer temperature is used in a polynomial model to provide compensation for all the coefficients used to convert the frequency counts into output units. Thus, the scale factor, bias and misalignment of the sensor axes are corrected over the entire temperature range.
The demodulation of the frequency sample is straightforward once the data is gathered each quarter cycle. The cosine demodulation is simply the difference between the appropriate half cycles. The linear acceleration is the sum of all samples.
The state of the art in micromachined rate and acceleration sensors is represented by U.S. Pat. No. 5,341,682 which is commonly assigned to the assignee of the present invention and incorporated herein by reference. The rate of rotation of a moving body about an axis may be determined by mounting an accelerometer on a frame and dithering it, with the accelerometer's sensitive axis and the direction of motion of the frame both normal to the rate axis about which rotation is to be measured. A Coriolis acceleration is the measure of the acceleration developed while the body is moving in a straight line and the frame upon which it is mounted rotates about the rate axis. The amplitude of the Coriolis component can be produced by vibrating or dithering the accelerometer, causing it to dither back and forth along a line perpendicular to the input axis of the accelerometer. When the frame upon which the accelerometer is mounted is rotated, the Coriolis acceleration component of the accelerometer's output signal increases in proportion to the dither velocity.
The linear acceleration component and the rotational component representing the Coriolis acceleration may be readily separated by using two accelerometers mounted in back-to-back relationship to each other and processing their output signals by sum and difference techniques as described in U.S. Pat. No. 4,590,801, which is commonly assigned to the assignee of the present invention and incorporated herein by reference.
Rate and acceleration sensors, for example, U.S. Pat. No. 5,341,682, are comprised of two accelerometers aligned in a single plane such that the input or sensitive axes of the two accelerometers are parallel and the output or hinge axes of the two accelerometers are parallel. The two accelerometers are vibrated or dithered at a predetermined frequency along a dither axis parallel to the hinge axes. The two accelerometers tend to vibrate at slightly different frequencies due to slight mass mismatch. Even if driven by a drive signal of common frequency, the accelerometer motions tend to be out of phase with each other. A link is connected to each of the two accelerometers whereby motion imparted to one accelerometer results in like but opposite motion imparted to the other accelerometer. Thus, the dithering motion imparted to one accelerometer is ideally of the exact same frequency and precisely 180 degrees out of phase with that applied to the other accelerometer.
The link provides an interconnect between the two accelerometers which is stiff in the dither axis such that the motion imparted to one accelerometer is effectively transmitted to the other accelerometer and both accelerometers ideally dither at the same frequency and precisely 180 degrees out of phase. The link is pivotally fixed to the frame by a pivot flexure. The link is further connected to each of the two accelerometers by flexures. The link is typically formed in a complex asymmetric shape. The complexity of the link is driven by practical considerations involved in adapting the link to accommodate both the pivot flexure and the two link-to-accelerometer flexures. The link's complex asymmetric shape provides adequate clearance between the link and the frame for the pivot flexure. The link's shape also provides adequate clearance between the link and each accelerometer to provide the precise flexure length to ensure that the flexures exhibit a predetermined mix of simple arc bending and "S-bend" motion and to ensure that any motion imparted to one accelerometer by the flexures is imparted to the other accelerometer as a sinusoidal function without introducing a higher order harmonic into the translation motion.
Although the device described in above referenced U.S. Pat. No. 5,341,682 functions for the purposes intended, its exact behavior is difficult to predict and/or model analytically. For example, the complex shape of prior links results in spring rates which are asymmetrical and a shape which is difficult to solve analytically. Additionally, constructing the shape previously taught results in flexures whose thicknesses and hence vibration properties are difficult to control.
Above referenced U.S. application Ser. No. 09/016,186 provides a linkage between accelerometers in a micromachined rate and acceleration sensor which is relatively simple to solve analytically and results in flexures whose thicknesses are relatively insensitive to process variations. For example, according to one aspect of U.S. application Ser. No. 09/016,186, the link shape can be solved using classical mechanical equations. According to another aspect of the invention, the present invention provides a shape which is relatively insensitive to process variations by providing a relatively simple shape having a symmetrical configuration. U.S. application Ser. No. 09/016,186 provides a simple symmetrically shaped link having sufficient mechanical stiffness in the to effectively transmit motion imparted to one accelerometer to the other accelerometer such that both accelerometers dither at the same frequency and precisely 180 degrees out of phase.
U.S. application Ser. No. 09/016,186 provides a simple symmetrical link which provides adequate clearance between the link and each accelerometer for flexures having a length which ensures that the flexures exhibit a predetermined mix of simple arc bending and "S-bend" motion and which ensures that any motion imparted to one accelerometer by the flexures is imparted to the other accelerometer as a sinusoidal function without introducing a higher order harmonic into the translation motion. U.S. application Ser. No. 09/016,186 provides a simple symmetrical link having reduced sensitivity to vibration in the dither cross-axis by providing, for example, a simplified columnar shaped. U.S. application Ser. No. 09/016,186 provides a simple symmetrical link having reduced sensitivity to cross-axis vibration by providing, for example, a link having a columnar shape in the dither cross-axis.
As described in U.S. Pat. No. 5,341,682, the accelerometers are suspended from a dither or mounting frame by a pair of flexures or "dither legs" which vibrate upon application of a dithering force to translate the accelerometers in a predominantly linear relationship with each other. However, true orthogonality is not achieved between the dither motion and the Coriolis acceleration sensing direction in the normal manufacturing process. State of the art micromachined vibrating Coriolis rate and acceleration sensors, as represented by U.S. Pat. No. 5,341,682 and others of the above incorporated patents and patent applications, experience quadrature motion due to the manifold sources of mechanical imperfection resulting from the tolerances inherent in manufacturing processes. This axis misalignment in conjunction with a phase shift causes a rate bias error which limits performance.
One method and apparatus for overcoming the errors introduced by quadrature motion is described in co-pending U.S. Pat. No. 5,886,259, assigned to the assignee of the present invention, steers the accelerometer input axes to be orthogonal using capacitive attraction between the sensing mass and stationary members of the sensor frame. However, such capacitive steering requires very small gaps, on the order of microns, between the sensing mass and stationary members to generate sufficient applied force. Given the very small gaps necessary, actual implementation of this axis alignment feature is difficult in a normal manufacturing setting using conventional processing methods.